Tuesday, June 18, 2019

A Tale of Colossal Stupidity

After my recent string of (fairly) successful constructions with heptominoes, I had started to get a craving for something even more challenging - and the octominoes were the next logical step. Now, I don't actually own a set of these, but for whatever reason I wasn't going to let something like that get in the way of my fun.
My brilliant idea was as follows - get an image of the 369 octominoes open in one instance of good ol' Microsoft Paint, then get a canvas shaped like the solution I was trying for (in this case, a 29x102 rectangle with six holes) in another. I'd then draw in each piece, deleting it from the piece-list as I went.

Here's a screenshot from part way through my attempt. Solution so far on the left, Pieces remaining on the right.
And for a while this seemed to work swimmingly. Okay, sometimes it was an absolute nightmare finding a piece on the right-hand screen to make sure I hadn't already used it, but aside from that it wasn't much harder than how I'd imagine using actual physical pieces would be. I knew that in the very late stages of the solution, the constant backtracking and retrying would be a ball-ache to say the least, but that was a bridge I was prepared to cross when I came to it.

I got within 11 pieces of completing the thing completely, when I began to feel like something was a wee bit off. And sure enough, on counting the squares left in the remaining area left to fill, I noticed it had 89 squares. At first I thought this could just be something with a perfectly reasonable explanation behind it; a piece with a hole left to place, or something like that. But as I looked at the pieces remaining it became clear what I'd done.

My heart sank.

There was only one plausible explanation for this - at some point during the long late-evening session the previous day, in which I'd done the bulk of this solution, I must have drawn a piece in incorrectly due to tiredness. Somewhere, in that writhing mass of 358 shapes was a lone heptomino, camouflaged almost perfectly. I went back through the pattern, checking each piece to make sure it was made up of eight squares, and colouring in each to mark it off as I checked it. Hopefully the offending piece will be close to the bottom so I don't have to backtrack too far... I repeated to myself as I worked my way through piece by piece, checking and double checking.

But it wasn't.

(Click on the image to feel the disappointment in all its full-size glory.)
In blue are the pieces I checked, and in red is the heptomino that managed to sneak in undetected. And at this point, after considering the hours I'd sunk into this to get this far and the countless more I'd have to spend to complete it, I just packed it in on the spot, gave it up as a bad job.

Octominoes are just gonna have to wait for another time, I think.

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